Giving our graphs some dimension, to day we expand our graphs from a 2D system to a 3D system with x-axis, y-axis, and z-axis. No longer are we constrained to four quadrants as now we can graph lines, curves, planes, and 3D shapes in all eight octants. Additionally, we look at vectors in 3D. All the operations and processes that we can do with vectors in a plane (2D vectors) we will now perform on vectors in space (3D vectors). Visually appealing fun stuff!

Objectives

By the end of this topic you should know and be prepared to be tested on:

13.2.1 Know terminology related to a 3D axis system (eg. yz-plane) and understand what it means to be a right-handed system

13.2.2 In a 3D system plot points, find distance between two points, find the midpoint of the line segment spanning two points

13.2.3 Given the equation of a plane, sketch it on a 3D system

13.2.4 Given the sketch of a plane in 3D or given information about a plane in 3D, find its equation

13.2.5 Determine from the sketch and/or equations if two planes are parallel or not

13.2.6 Given the equation of a sphere or ball, sketch it on a 3D system

13.2.7 Given the sketch of a sphere or ball in 3D or given information about a sphere or ball in 3D, find its equation

13.2.8 Perform vector operations on vectors in 3D

13.2.9 Do all the things that we learned to do on 2D vectors in the plane now on 3D vectors in space including find magnitude, direction, and a unit vector in the direction of a given vector

3D Vector Plotter from Acedemo is user-friendly free software to display 3D vectors, make adjustments to see the effect, and spin to view from different perspectives. Academo also has a limited but easy-to-use 3D Surface Plotter.

Patrick JMT Just Math video tutorials: PatrickJMT.com/#calculus
I'm not recommending this site today since the vector examples tend to be 2D, not 3D. Instead see ...

James Sousa's Math Is Power 4U video tutorials: MathIsPower4U - Calc II
Scroll down the third column to the "Vectors in Space" category. The first 10+ vectors listed are useful for this unit. Stop at "Dot Product" which is covered in our next unit.